My purely anecdotal (but very extensive) experience is that the typical conspiracy believer is a person of normal or better intelligence but with a limited or very narrow education.
Some observations: There seem to be some very characteristic gaps in this group’s general cultural knowledge as well. History, geography, and mathematics seem to be the areas of which they are most strikingly and consistently ignorant. I am still not sure what to make of this but I have seen this same pattern occur over and over.

I’ve mentioned the Moon hoax conspiracy believer I met who did not realize that there is more than one national military force in the world. This emerged from her response to my point that military forces all over the world could have tracked the Apollo missions and at least some of them would immediately have exposed a hoax. She thought this was impossible because they would all do as they were told. I said I was talking about foreign military forces. She had no idea what I meant by that and it took some more back and forth to figure out what the problem was: She literally believed that only the United States had military forces. I asked her if she had never heard of, say, the British army. She said, oh sure but that was way back in George Washington’s time.
She had no idea when that was, btw, except that cars apparently had not been invented yet since they all rode horses. This person was a senior in college, a pre-med student in fact.